Brad:
I am headed to Taiwan again this December...
I have travelled to Taiwan many times with my stock Verizon Samsung Galaxy S3. Once I land, I simply insert a local telecom SIM card (Chunghwa Telecom) and all the call functions worked just fine, except for the data connection bit.. NO GO unless you can root and do a bit of work around... there is a thread in this forum explaining how to do that so Verizon Galaxy S3 will work on other data network. It's worth your while if it's an AT&T phone, for the bands on that version of Galaxy S3 are more compatible with those used in Taiwan... Verizon claims the S3 is unlocked - which is only partially true.. It's unlocked for the voice part of the phone to work but not the data connection outside of Verizon network.
Chunghwa Telecom is the biggest and offered the most coverage in Taiwan. Incidentally, I inserted the same SIM card into my Nexus 7 - and the data connection worked fine, albeit it was so slow that I preferred the WiFi.. It could because I was in the country.
I simply buy a prepaid Chunghwa telecom SIMS (available at the Taipei Airport once you land (the counter closes at 9:00PM) or you can have someone in Taiwan take you to a Chunghwa telecom retail to purchase one, be sure to have a driver's licence and a passport with you) .. Recharging is simple at the KIOSK at any 7-Eleven, which is everywhere...
I then, march over to "Family Mart", a chain convenience store in every corner (usually close to its competitor, 7-Eleven)- sometimes two within one block and purchase a Wi-Fi pass for $10 USD at the Kiosk - all you can use for one week, I think... Buy a new pass as you run out of time. I simply saved the new password on the WiFi connection setting on my phone and Nexus 7.
The amazing part is that the WiFi coverage is so wide - I seem to get signals wherever I go; and you are not limited to just the Family Mart, a lot of public places have Chunghwa telecom's WiFi hotspots.. Yes, 3G / 4G is more convenient, but in my 2-3 week stays, I don't miss my data connection that much.
7-Eleven (at every corner of the entire Island) offers free two-hour connections everyday - but it requires that you watch a short commercial before you can login... I simply connect my phone to the WiFi, order my coffee at the counter then I'd be ready to check my emails / post Instagram photos / update FB pages etc...
If you are in Taipei, the MRT (subway system) stations offer free Wifi - airports, train stations, coffee shops, etc offer many free hotspots... Some spots may be slow while I have seen improvements in speeds in the last three years of my travels in Taiwan. Because their living space is so close to each other in the cities, I often find plenty of free WiFi connections from apartments in the neighbourhood. It's not recommended to use them due to security concerns, of course.
Hope this helps. Let me know if you got any questions; I'm glad to help.
cheers,
jc
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